Much work concerning the prototypical problem of regression focuses on the study of rates of error of a given statistical procedure while making strong assumptions on the underlying distributions of samples, assuming for instance that they are i.i.d. and subgaussian or bounded (see for instance, [28, 41, 31]). It is however of fundamental importance to understand what happens when the data violates such strong assumptions, for instance, when the underlying distribution of samples is heavy-tailed and/or when the dataset is corrupted by outliers. In such cases - which are everyday cases for real-world datasets - classical estimators such as OLS or MLE exhibit, at best, far-from-optimal statistical behaviours and at worst completely non-sens outputs. In this work, we study the statistical properties (non-asymptotic estimations and predictions results) of algorithms coming with actual working code constructed on this type of real-word datasets. We want to put forward that it is an algorithm and not only a purely theoretical estimator and that this algorithm can be coded efficiently (we provide a simulation study in the following) since its most time consuming fundamental building block is to find a top singular vector of a reasonable size matrix. However, our theoretical results show that even though the dataset is far from the ideal i.i.d.

Graph Identification (GI) has long been researched in graph learning and is essential in certain applications (e.g. social community detection). Specifically, GI requires to predict the label/score of a target graph given its collection of node features and edge connections. While this task is common, more complex cases arise in practice---we are supposed to do the inverse thing by, for example, grouping similar users in a social network given the labels of different communities. This triggers an interesting thought: can we identify nodes given the labels of the graphs they belong to? Therefore, this paper defines a novel problem dubbed Inverse Graph Identification (IGI), as opposed to GI. Upon a formal discussion of the variants of IGI, we choose a particular case study of node clustering by making use of the graph labels and node features, with an assistance of a hierarchical graph that further characterizes the connections between different graphs. To address this task, we propose Gaussian Mixture Graph Convolutional Network (GMGCN), a simple yet effective method that makes the node-level message passing process using Graph Attention Network (GAT) under the protocol of GI and then infers the category of each node via a Gaussian Mixture Layer (GML). The training of GMGCN is further boosted by a proposed consensus loss to take advantage of the structure of the hierarchical graph. Extensive experiments are conducted to test the rationality of the formulation of IGI. We verify the superiority of the proposed method compared to other baselines on several benchmarks we have built up. We will release our codes along with the benchmark data to facilitate more research attention to the IGI problem.

This is a part of a series of blogs where I'll be demonstrating different aspects and the theory of Machine Learning Algorithms by using math and code. This includes the usual modeling structure of the algorithm and the intuition on why and how it works, using Python code. Logistic Regression is one of the first algorithms that is introduced when someone learns about classification. You probably would have read about Regression and the continuous nature of the predictor variable. Classification is done on discrete variables, which means your predictions are finite and class-based like a Yes/No, True/False for binary outcomes.

Converting dates to numbers is important because while time is essential for a model's consideration, it cannot handle datetime objects. Instead, time can be represented as an integer. The majority of a data science project comprises of data cleaning and manipulation. Images created by author unless explicitly stated otherwise. Missing values often plague data, and given that there are not too many of them, they can be imputed (filled in).

In this article, we will build a logistic regression model for classifying whether a patient has diabetes or not. The main focus here is that we will only use python to build functions for reading the file, normalizing data, optimizing parameters, and more. So you will be getting in-depth knowledge of how everything from reading the file to make predictions works. If you are new to machine learning, or not familiar with logistic regression or gradient descent, don't worry I'll try my best to explain these in layman's terms. There are more tutorials out there that explain the same concepts.

Learn to build a Polynomial Regression model to predict the values for a non-linear dataset. In this article, we will go through the program for building a Polynomial Regression model based on the non-linear data. In the previous examples of Linear Regression, when the data is plotted on the graph, there was a linear relationship between both the dependent and independent variables. Thus, it was more suitable to build a linear model to get accurate predictions. What if the data points had the following non-linearity making the linear model giving an error in predictions due to non-linearity? In this case, we have to build a polynomial relationship which will accurately fit the data points in the given plot.

I assume you already know what regression is. "Regression is a statistical method used in finance, investing, and other disciplines that attempts to determine the strength and character of the relationship between one dependent variable (usually denoted by Y) and a series of other variables (known as independent variables)." In the most simple terms -- we want to fit a line (or hyperplane) through data points to obtain a line of best fit. The algorithm behind aims to find the line which minimizes the cost function -- typically MSE or RMSE. That's linear regression, but there are other types -- like polynomial regression.

The processing power required to extract value from the unmanageable swaths of data currently being collected, and especially to apply artificial intelligence techniques such as machine learning, keeps increasing. Researchers have been trying to figure out a way to expedite these processes applying quantum computing algorithms to artificial intelligence techniques, giving rise in the process to a new discipline that's been dubbed Quantum Machine Learning (QML). Quantum Computing: How it differs from classical computing? The race to make good on quantum computing is well underway. Millions of dollars have been allocated to developing machines that could cause current computers to become obsolete.

Autonomous and semi-autonomous systems for safety-critical applications require rigorous testing before deployment. Due to the complexity of these systems, formal verification may be impossible and real-world testing may be dangerous during development. Therefore, simulation-based techniques have been developed that treat the system under test as a black box during testing. Safety validation tasks include finding disturbances to the system that cause it to fail (falsification), finding the most-likely failure, and estimating the probability that the system fails. Motivated by the prevalence of safety-critical artificial intelligence, this work provides a survey of state-of-the-art safety validation techniques with a focus on applied algorithms and their modifications for the safety validation problem. We present and discuss algorithms in the domains of optimization, path planning, reinforcement learning, and importance sampling. Problem decomposition techniques are presented to help scale algorithms to large state spaces, and a brief overview of safety-critical applications is given, including autonomous vehicles and aircraft collision avoidance systems. Finally, we present a survey of existing academic and commercially available safety validation tools.

Public transportation plays a critical role in people's daily life. It has been proven that public transportation is more environmentally sustainable, efficient, and economical than any other forms of travel. However, due to the increasing expansion of transportation networks and more complex travel situations, people are having difficulties in efficiently finding the most preferred route from one place to another through public transportation systems. To this end, in this paper, we present Polestar, a data-driven engine for intelligent and efficient public transportation routing. Specifically, we first propose a novel Public Transportation Graph (PTG) to model public transportation system in terms of various travel costs, such as time or distance. Then, we introduce a general route search algorithm coupled with an efficient station binding method for efficient route candidate generation. After that, we propose a two-pass route candidate ranking module to capture user preferences under dynamic travel situations. Finally, experiments on two real-world data sets demonstrate the advantages of Polestar in terms of both efficiency and effectiveness. Indeed, in early 2019, Polestar has been deployed on Baidu Maps, one of the world's largest map services. To date, Polestar is servicing over 330 cities, answers over a hundred millions of queries each day, and achieves substantial improvement of user click ratio.